function cov_plot = plot_cov_over_nu(empirical_cov_list, meta_nu_list, EB_nu)
    
    cov_plot = figure;
    set(cov_plot, 'Units', 'inches', 'Position', [1 1 5.833 4.373]); 
    hold on;
    
    % Plot each line with a unique color and set display names for the legend
    plot(meta_nu_list, empirical_cov_list, 'k', 'LineWidth', 1.2);
    
    % Find the y-value at EB_nu using interpolation
    y_value = interp1(meta_nu_list, empirical_cov_list, EB_nu);
    plot(EB_nu, y_value, 'x', 'Color', 'k', 'MarkerSize', 12, 'LineWidth', 1.5, 'HandleVisibility', 'off');
                
    % Find intersections with y = 0.8
    for j = 1:length(meta_nu_list) - 1
        % Check if there is a crossing at y = 0.8 between two consecutive points
        if (empirical_cov_list(j) - 0.8) * (empirical_cov_list(j + 1) - 0.8) < 0
            % Interpolate to find the exact x-value of the intersection
            x_intersect = interp1(empirical_cov_list(j:j+1), meta_nu_list(j:j+1), 0.8);
            
            % Plot the intersection point on the line with a small circle
            plot(x_intersect, 0.8, 'o', 'Color', 'k', 'MarkerSize', 10, 'LineWidth', 1.5, ...
                 'HandleVisibility', 'off');     
        end
    end

    % Add a dashed reference line at y = 0.8
    yline(0.8, 'k--', 'LineWidth', 1, 'HandleVisibility', 'off');
    % Get current y-axis limits
    currentYLim = ylim;
    % Set the new upper limit while keeping the lower limit the same
    ylim([currentYLim(1), 1]);

    % Add xticks
    xtick = 0:0.1:0.5;
    xticks(xtick);
    xlim([xtick(1), xtick(end)]);

    ytick = 0.5:0.1:1;
    % ytick = 0.6:0.1:1;
    yticks(ytick);
    ylim([ytick(1), ytick(end)]);
    set(gca, 'FontSize', 18);
    set(gca, 'TickLabelInterpreter', 'latex');
    
    hold off;

end